Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#3

Question i.       Sketch the curve ii.      The region enclosed by the curve, the x-axis and the y-axis is rotated through 360◦ about the x-axis. Find the volume obtained, giving your answer in terms of . Solution      i.   Standard form of quadratic equation is; The graph of quadratic equation is a parabola. If  (‘a’ is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#10

Question i.       Express  in the form  and hence state the coordinates of the minimum point, A, on the curve . The line  intersects the curve  at points P and Q. It is given that the coordinates of P are (3,7).    ii.       Find the coordinates of Q.   iii.       Find the equation of the line joining Q to the mid-point of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#9

Question In the diagram, OAB is an isosceles triangle with  and angle  radians. Arc PST has centre O and radius , and the line ASB is a tangent to the arc PST at S.     i.       Find the total area of the shaded regions in terms of  and .    ii.       In the case where  and , find the total perimeter […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#7

Question A curve is such that  and the point  lies on the curve. i.       Find the equation of the curve.    ii.       Find the set of values of x for which the gradient of the curve is less than . Solution     i.   We can find equation of the curve from its derivative through integration; For the given case; Therefore; Rule […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#6

Question The variables x, y and s can take only positive values and are such that  and     i.       Show that .    ii.     Find the stationary value of  and determine its nature. Solution     i.   We are given that; We are also given that; We can find out y from this equation; Substituting this value of y in;   ii.   […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#5

Question      i.       Show that the equation   can be written in the form    ii.        Hence solve the equation  for . Solution i.   We have the equation; We have the relation , therefore, Multiplying entire equation with We have the trigonometric identity; We can rewrite it as; Therefore;      ii.   To solve the equation  , […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#4

Question The diagram shows a prism ABCDPQRS with a horizontal square base APSD with sides of length 6 cm. The cross-section ABCD is a trapezium and is such that the vertical edges AB and DC are of lengths 5 cm and 2 cm respectively. Unit vectors ,  and  are parallel to AD, AP and AB respectively. i.       Express each of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#2

Question The volume of a spherical balloon is increasing at a constant rate of 50 cm3 per second. Find the rate of increase of the radius when the radius is 10 cm. [Volume of a sphere ] Solution      i.   We are given that; We are required to find rate of change of radius; Therefore; For rate of change of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#11

Question Functions  and  are defined for  by      i.       Find and simplify expressions for  and .    ii.       Hence find the value of a for which .   iii.       Find the value of  for which .   iv.       Find and simplify an expression for . The function  is defined by  ,    v.       Find an expression for . Solution i.   We have functions; We can write these […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#1

Question Find the coefficient of  in the expansion of  . Solution Expression for the Binomial expansion of  is: In the given case: Hence; The coefficient of   is .

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#8

Question A television quiz show takes place every day. On day 1 the prize money is \$1000. If this is not won  the prize money is increased for day 2. The prize money is increased in a similar way every day  until it is won. The television company considered the following two different models for increasing  the prize money. […]